Question Number 170255 by mathlove last updated on 19/May/22 $$\frac{{d}}{{dx}}\left[\int_{\mathrm{2}} ^{{x}} {e}^{{t}^{\mathrm{2}} } {dt}=?\right. \\ $$ Answered by floor(10²Eta[1]) last updated on 19/May/22 $$\int_{\mathrm{2}} ^{\mathrm{x}}…
Question Number 104718 by M±th+et+s last updated on 23/Jul/20 $$\int{tan}^{−\mathrm{1}} \left(\frac{{a}\sqrt{{x}}+{b}}{{c}}\right){dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 23/Jul/20 $$\int\frac{\mathrm{2}{c}\sqrt{{x}}}{{a}}{tan}^{−\mathrm{1}} {udu}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{u}=\frac{{a}\sqrt{{x}}+{b}}{{c}}\Rightarrow\frac{{a}}{\mathrm{2}{c}\sqrt{{x}}}=\frac{{du}}{{dx}} \\ $$$$\frac{\mathrm{2}{c}}{{a}}\int\sqrt{{x}}{tan}^{−\mathrm{1}}…
Question Number 39165 by math khazana by abdo last updated on 03/Jul/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}\:} \:+{t}^{\mathrm{6}} } \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on…
Question Number 39135 by maxmathsup by imad last updated on 02/Jul/18 $${calculate}\:{A}\left(\lambda\right)\:=\:\int_{\mathrm{0}} ^{\lambda} \:\:\:\frac{{ln}\left({x}+\sqrt{\left.\mathrm{1}+{x}^{\mathrm{2}} \right)}\right.}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left({x}+\sqrt{\left.\mathrm{1}+{x}^{\mathrm{2}} \right)}\right.}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$ Commented…
Question Number 170189 by SLVR last updated on 18/May/22 Commented by SLVR last updated on 18/May/22 $${I}\:{could}\:{not}\:{find}\:{b},\:{c}\:,{d},{e}…{kidly} \\ $$$${help}.. \\ $$ Commented by SLVR last…
Question Number 39120 by math khazana by abdo last updated on 02/Jul/18 $${let}\:{A}_{{n}} =\:\int_{\mathrm{1}} ^{{n}} \:\frac{\left[\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right]\:−\left[{x}\right]}{{x}^{\mathrm{2}} }\:{dx}\:\:\left({n}\:{integr}\:\geqslant\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \: \\…
Question Number 39119 by math khazana by abdo last updated on 02/Jul/18 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}^{\mathrm{2}} \:{cos}\left(\mathrm{4}{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by math khazana by…
Question Number 104644 by Rohit@Thakur last updated on 22/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}} \right){dx}}{{x}}\:=\:−\frac{\pi^{\mathrm{2}} }{\mathrm{15}} \\ $$ Answered by mathmax by abdo last updated…
Question Number 104645 by Dwaipayan Shikari last updated on 22/Jul/20 Commented by Aziztisffola last updated on 22/Jul/20 $$\mathrm{How}\:\mathrm{to}\:\mathrm{post}\:\mathrm{a}\:\mathrm{topic}\:\mathrm{with}\:\mathrm{this}\:\mathrm{app}? \\ $$$$\mathrm{thanks}. \\ $$ Answered by Ar…
Question Number 104609 by M±th+et+s last updated on 22/Jul/20 $${prove}: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{4}} \left(\mathrm{1}−{x}\right)^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\mathrm{22}}{\mathrm{7}}−\pi \\ $$ Answered by Dwaipayan Shikari last updated…